Ion Velocity Fourier Transform Mass Spectrometry

Eugene Nikolaev, Sergey Rakov and Jean Futrell

Introduction
A new concept is proposed for mass spectrometry based on Fourier transform analysis of the detected image current generated by ions with a certain velocity ensemble. The induced charge density function developed by a single ion traveling in an infinitely long tube electrode is derived. Electrostatic ion beam guide designs for linear and cyclic-orbit trajectory mass analyzers are proposed. Computer simulations using MATLAB 4.2 and SIMION 6.0 interfaces were performed to support the proposed designs in terms of field distribution and ion trajectory dynamics.

The idea of using an induced charge as a signal source for FT analysis has been used routinely in Fourier Transform Ion Cyclotron Resonance. Conventional FT ICR cells use two detection electrodes systems. Orbiting charged particles induce the current between the two detection plates. The current undergoes Fourier transformation and is presented in the form of the mass spectrum. Systems with more then one pair of detectors have also been studied, [1],[2].

We designed and studied a detector which implements the idea of periodic induced current detection for mass analysis without the drawbacks of requiring high magnetic fields. Here we present four possible geometries for the FTIV MS which adequately illustrate the concept and applications: (1) the field free linear periodic ring detector array, (2) the stacked lens ion guide, (3) spherical ion trap periodic detector array [3], and (4) cylindrical ion trap periodic detector array. They are discussed it terms of induced current function, beam packet dissipation and the resulting resolution restrictions. Computer simulations are provided where necessary. Although these four examples are not the only geometry designs suitable for the implementation of the technique, they adequately illustrate the possibilities and advantages of FT IV MS.

General Approach

In all the cases we pose the same initial conditions-, namely, we start with a point source of monochromatic ions with a given angular divergence at the entrance of the detecting array. For each detector geometry we calculate the potential distribution along the beam path. In most geometries we can analytically calculate the ion trajectories. Simultaneously the induced charge as a function of ion position inside the detector is derived. Summation for all the electrodes inside the same group follows. Combining these results we obtain an induced charge density function as a function of time. Taking its time derivative we get the induced current. As we expand it in Fourier series we immediately obtain the frequency spectrum, which is finally transformed in the mass spectrum.

Next we examine the phase divergence of the beam (natural broadening of the spectral lines) for this particular design of ion guide and consider how to decrease it. Careful derivation of aberration coefficients and computer simulations are important at this stage of analysis. Prediction of resolving power is then obtained as a convolution of broadening and ideal resolution. There are several general sources of broadening of an initially monochromatic beam:

Aberrational properties which cause the broadening for each of the ion guides considered are typical for a given geometry.

Realization and Resolution Predictions

The simplest way to implement this concept is to construct a periodic linear array of detecting plates or rings which will generate the required ion velocity signal is shown below: Redistribution of the charge induced by a single moving charge in the periodic array of detecting electrodes provides information about the ion's velocity. As the resolution of a Fourier transform is proportional to the number of periods in the time domain one must provide a reasonably large number of detecting pairs in the array for resolution to be of practical value. This suggests longer detectors. However, the unfortunate effect of initial divergences of the incoming beam on the ultimate resolution cannot be eliminated even by beam focusing using periodic Einzel lens arrays (discussed in [2] and shown in Fig. below:) Guiding-detecting electrode groups marked as 1 and 2 are disconnected in a DC sense and shorted through an operational amplifier in the AC sense using well known ICR circuitry. The performance of this type of array is illustrated in Figs below:

The three diverging modulated curves in the second Fig. reflect accumulation of the axial divergence, dx (Fig 1 in the later set), by three ions with different starting angles in a diverging monochromatic beam. As soon as dx becomes larger then the array cell constant, L, the detected signal is out of phase (broadened by 2pi) and further detection is senseless.

Linearity of the overall axial divergence of the three curves in Figs above insures that only the first-order alpha-aberrations are present. Small nodes in the curves correspond to the array cell constant, L and introduce multiple-harmonics distortion in detected signal. The larger node is caused by focusing properties of the potential array which depend on geometry and voltages applied to the lens groups. It introduces only one easily predictable extra harmonic of a much lower frequency.

Restricted trajectory ion guides - namely, spherical analyzer ion guide and cylindrical analyzer ion guide - are shown in Figures below:

Next set of figures illustrates some aspects of physics involved in characterization of the restricted-trajectory guides. Strong advantage of this family of ion guides comes with realizability of "infinite" ion trajectories, compact size and mechanical simplicity. Analytical studies of trajectories and resolving power predictions are only slightly more complex and the same major limitations apply.

Summary

Simulations of linear geometry array detectors utilizing stacked-lens ion guides have shown that resolving power of 10^3 is easily achieved for a reasonable scale design (array length ~5m). Simplicity of design, linear relationship between resolving power and tube length, and simple control of beam divergence can be mentioned as advantages of this class of instruments.

Introducing the added complexity of the HV pulsed-gates to inject ions into confined - trajectory ion guides (electrostatic traps or analyzers) removes the limitations of the array size on the achievable resolving power. Background beam dephasing and storage of the detected signal become significant considerations. Despite these limitations simulations predict resolution of 10^3-10^4 for desktop size models of the spherical and cylindrical analyzer guides.

Overall FTIV MS appears to be a plausible alternative to B-field based MS and conceptional TOF MS. Applications may include environmental MS measurements for instruments of the confined trajectories class, where resolution can be somewhat sacrificed for compact size, mechanical simplicity and low power requirements. An exotic potential application (astrophysics) of the linear geometry example is detection of a single charged particle under conditions of ultra-low background pressure.

Key References